Abstract: Based on the 6×6 Luttinger-Kohn Hamiltonian,including strain,and taking into account of the quantum-size effect and spin-orbit coupling,a band structure model for p-type silicon nanoplate piezoresistors is established using the finite difference method.The effect of thickness,impurity concentration,and temperature on the piezoresistive coefficient of the silicon nanoplate was quantitatively investigated based on its dependence on the band structure.The results indicate that the effect of the quantum confinement of holes,which dramatically alters the band structure,enhances the piezoresistive coefficient of the p-type silicon nanoplate piezoresistors.The spin-orbit coupling,which changes the band-edge energies,plays a significant role in the high strained silicon nanoplates.The size-dependent piezoresistive coefficient of the p-type silicon nanoplate piezoresistors increases as the thickness decreases.The piezoresistive coefficient was also observed to decrease with increased impurity concentration and temperature.In the extreme degenerate range,the piezoresistive coefficient is controlled only by the impurity concentration and becomes temperature-independent.In the non-degenerate range,the opposite phenomenon occurs.Furthermore,according to the form change of constant energy surfaces for heavy and light holes in the presence of stress,we qualitatively analyze the origin of the longitudinal piezoresistive effect in the silicon nanoplate.

Key words: silicon, band structure, piezoresistive, quantum size-effect, spin-orbit coupling